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Midterm Exam - Formula Sheet Quartiles

Q1 =



 25 (n + 1) value 100

Q3 =



 75 (n + 1) value 100

Median and IQR If n is odd, Median =



n+1 2



obs IQR = Q3 − Q1

If n is even   (n/2)obs + ((n/2) + 1)obs Median = 2 Fence for outliers • Lower Fence = Q1 − 1.5 × (Q3 − Q1 ) • Upper Fence = Q3 + 1.5 × (Q3 − Q1 )

Mean and Sample Standard Deviation

x¯ =

Pn

i=1

xi

s=

n

sP

n i=1 (xi

− x¯)2 n−1

Probability Rules

General Addition Rule Independent Events Mutually Exclusive Events Conditional Probability

P (A ∪ B) = P (A) + P (B) − P (A ∩ B )

P (A ∩ B) = P (A)P (B ) P (A ∩ B) = 0

P (A/B) = P (A ∩ B)/P (B)

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ECON 2B03

Midterm

Winter 2020

Distributions

Distribution

Function

E(X) V(X)

Binomial Distribution

P (X = m) = nCm × pm × q n−m

np

npq

Poisson Distribution

Pλ (x) =

λ

λ

Exponential Distribution

FX (x) = 1 − e−λx

1/λ

1/λ2

e−λ λx x!

Permutation and Combination Ordered Selection nP r =

Unordered Selection n! (n − r)! Normal Distribution

nCr =

n! r!(n − r)!

X ∼ N (µ, σ) For a sample of size n

X −µ Z= ∼ N (0, 1) σ

Z=

¯ −µ X √ ∼ N (0, 1) σ/ n

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